A doubly restricted exponential dispersion model

Abstract

In this paper, we propose and develop a doubly restricted exponential dispersion model, i.e. a varying dispersion generalized linear model with two sets of restrictions, a set of linear restrictions for the mean response, and at the same time, for another set of linear restrictions for the dispersion of the distribution. This model would be useful to consider several situations where it is necessary to control/analyze drug-doses, active effects in factorial experiments, mean-variance relationships, among other situations. A penalized likelihood function is proposed and developed in order to achieve the restricted parameters and to develop the inferential results. Several special cases from the literature are commented on. A simply restricted varying dispersion beta regression model is exemplified by means of real and simulated data. Satisfactory and promising results are found.

Keywords:

• Beta distribution
• two-parameter exponential family
• generalized linear models
• linear restrictions
• maximum likelihood estimation
• penalized likelihood
• varying dispersion

Additional information

Funding

Luis Fernando Grajales heads the Research Group Mtodos en Bioestadística (COL0034469). Luis Fernando Grajales, Luis A. López, and Oscar O. Melo belong to the Research Group Estadística Experimental Aplicada a la Investigacin, la Industria y la Biotecnología (COL0004469), both Groups supported by COLCIENCIAS (Colombia). RO thanks to CNPq, and FACEPE, Brazil.